Multiply the following complex numbers: $({-3i}) \cdot ({3})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3i}) \cdot ({3}) = $ $ ({0} \cdot {3}) + ({0} \cdot {0}i) + ({-3}i \cdot {3}) + ({-3}i \cdot {0}i) $ Then simplify the terms: $ (0) + (0i) + (-9i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 - 9)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 - 9)i - 0 $ The result is simplified: $ (0 - 0) + (-9i) = -9i $